Sheila and Katherine Lyon
Montgomery County, Md., Police Department/AP
For nearly 40 years, the disappearance of sisters Sheila, 12, and Katherine Lyon, 10, last seen near a shopping mall, has baffled the girls' family and the surrounding community of Kensington, Md.
But there may finally be a break in the case. Detectives are hoping to gather more evidence that might link the disappearance to Lloyd Lee Welch, 57, a currently incarcerated sex offender who once worked as a carnival ride operator.
"The Lyons are an all-American family who were so devastated after the girls disappeared," former next-door neighbor Winifred Leesnitzer, 84, tells PEOPLE. "Hopefully the case will be solved now so their daughters can finally rest in peace."
Police on Tuesday said Welch was at the Wheaton Plaza mall on March 25, 1975, the same day the girls vanished, and that he seemed to pay close attention to them.
"We need everyone who may know something to come forward," Steve Vogt, FBI Baltimore Division special agent in charge, said Tuesday. "It might be enough to put the pieces of this puzzle together."
The Lyon family issued a statement thanking the community for never giving up. "March 25th will mark 39 years since Kate and Sheila were taken from our family," the statement says. "We are grateful for any information the public can provide to help bring this story to its conclusion."
The girls' parents, Jon, 74, a former radio personality, and Mary Lyon, 74, a homemaker, still reside in the same family home in Kensington. The sisters' older brother, Jay Lyon, who was 15 at the time and reportedly one of the last to see them alive, went on to become an officer with the local police department.
"I suspect the loss of his sisters was the motivation for Jay to join the police force," retired Montgomery County Police detective Harry Geehreng tells PEOPLE. "I think it changed his life forever. Over time, I think the Lyon family just withdrew and tried to grieve in private. I think they just tried to return to normal life as best they could."
While Welch is not due for release until 2027, a hearing is scheduled for July on his request for early release, the Washington Post reported
Police say that Welch, 18 at the time, became a more obvious potential suspect over the years as he got picked up for other offenses.
When Welch was arrested for burglary in 1977, his mug shot resembled an old police sketch of a stranger described by a girlfriend of the Lyon sisters who saw a man following the three of them that day. When detectives recently took a fresh look at the case a few months ago, Welch "jumped out at us," said Assistant Montgomery County Police Chief Russ Hamill.
A niece of Welch's tells the Post
that Welch admits to being at Wheaton Plaza that day – but denies any involvement in the girls' disappearance.
"The only thing he said he did was walk around the mall," Debbie Roe, 38, of Dover, Del., tells the Post
. "I think they need to look elsewhere. He doesn't know where the girls are."